If the line joining points (2, 1, 4) and (a - 1, 4, -1) is parallel to the line joining points (0, 2, b - 1) and (5, 3, -2) then the values of b and a are respectively

Step-by-step solution

Direction ratios of the line joining (2, 1, 4) and (a - 1, 4, -1) are (a - 1 - 2, 4 - 1, -1 - 4) = (a - 3, 3, -5) . Direction ratios of the line joining (0, 2, b - 1) and (5, 3, -2) are (5 - 0, 3 - 2, -2 - (b - 1)) = (5, 1, -b - 1) . Since the lines are parallel, their direction ratios are proportional: a - 3 5 = 3 1 = -5 -b - 1 From a - 3 5 = 3 , we get a - 3 = 15 a = 18 . From -5 -b - 1 = 3 , we get -5 = -3b - 3 3b = 2 b = 2 3 . The values of b and a respectively are 2 3 , 18 . Answer: 2 3 , 18